Block #211,791

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/15/2013, 9:53:29 PM · Difficulty 9.9174 · 6,579,693 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

4da7aef0bb63413591a7f904c32497c93b99cdbfe822fa7ef639d35955109364

View on Chainz ↗

Height

#211,791

Difficulty

9.917409

Transactions

Size

4.43 KB

Version

Bits

09eadb54

Nonce

1,164,784,540

Timestamp

10/15/2013, 9:53:29 PM

Confirmations

6,579,693

Merkle Root

fed9c3e876cd6ebbb79a00dc6dc3fd939ee8aabb64a3f49d01c94954805dbc97

Transactions (1)

Coinbasefed9c3e876cd6e…c94954805dbc97

1 in → 129 out10.1000 XPM4.34 KB

AMFZUpsP…4akTRV6E ASTyaa89…LKTnQv8K Acf2JSx5…RJL8Z9QV AY2xJ15f…mp4Huewu AWVGtkZj…m321bzSA

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.025 × 10⁹³(94-digit number)

30257619812588433920…06413885241909787359

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

3.025 × 10⁹³(94-digit number)

30257619812588433920…06413885241909787359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.051 × 10⁹³(94-digit number)

60515239625176867841…12827770483819574719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.210 × 10⁹⁴(95-digit number)

12103047925035373568…25655540967639149439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.420 × 10⁹⁴(95-digit number)

24206095850070747136…51311081935278298879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.841 × 10⁹⁴(95-digit number)

48412191700141494273…02622163870556597759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.682 × 10⁹⁴(95-digit number)

96824383400282988546…05244327741113195519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.936 × 10⁹⁵(96-digit number)

19364876680056597709…10488655482226391039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.872 × 10⁹⁵(96-digit number)

38729753360113195418…20977310964452782079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.745 × 10⁹⁵(96-digit number)

77459506720226390837…41954621928905564159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer